Molecular-dynamics study of mechanical properties of nanoscale copper with vacancies under static and cyclic loading

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Abstract

A molecular-dynamics simulation of the mechanical properties of nanoscale copper with vacancies under static and cyclic loading has been carried out. From the tensile test, the stress–strain curve for nanoscale copper was obtained first and then the Young’s modulus of the material was determined. The Young’s modulus decreases with increasing vacancy fraction, and it also decreases with increasing temperature. It can be clearly seen that the ultimate tensile stress and elongation rate are high for nanoscale copper, and result in the high fracture energy required to break the nanoscale copper. From the fatigue test, the amplitude stress–number of cycles curve was obtained. Under the lower applied stress, the amplitude stress of the nanoscale copper increases with decreasing vacancy fraction, however, it decreases with decreasing temperature. Furthermore, the fatigue limit of the nanoscale copper increases with decreasing vacancy fraction and increasing temperature, when the material is under a less-than-critical value of applied stress.

Introduction

Over the past decade, the study of the mechanical properties of nanostructured materials using atomistic simulation has been of significant interest to researchers due to nano-technological development [1], [2], [3]. For example, Miyazaki and Shiozaki [4] calculated the elastic constant and thermal expansion coefficient of Fe. Aya and Nakayama [5] investigated the influence of environmental temperature on the yield stress of polymers. The material stiffness is one of the important properties of a material. Miller and Shenoy [6] studied the bending stiffness properties of nanosized structural Al and Si. Since the development of the electronic industry, copper has been one of the important materials in the field, used in, for example, electrical interconnects [7]. Many studies have look at the material properties of copper. Heino et al. [8] investigated the mechanical properties of copper, including the elastic constant and the behavior of crack propagation at room temperature. Schiotz et al. [9] studied the effects of strain rate and porosity on the mechanical deformation of copper at various temperatures. Recently, Kang and Hwang [10] investigated mechanical deformations of copper nanowire. Previous studies focused on the material behavior under a static loading. Only a limited portion of studies published were concerned with the aspect of cyclic loading. This is because the fatigue test for cyclic loading is a time-consuming task, especially when using an experimental method. Inoue et al. [11] studied the fracture mechanisms of nanoscale pure iron under static and cyclic loading using molecular dynamics simulation. Read [12] experimentally studied the tension–tension fatigue behavior of copper thin films at room temperature. Chen et al. [13] investigated the influence of temperature on the low cycle fatigue behavior of nickel-based superalloys, and found that the fatigue life does not monotonously decrease with increasing test temperature.

In this paper, using the molecular dynamics simulation [14], the tensile test and the tension–compression fatigue test for nanoscale copper with vacancies are carried out at various temperatures.

Section snippets

Analysis

In this paper, the Lennard–Jones potential model, which is still widely used, is also adopted for the calculation process. It isφr=4εσr12σr6where φ represents the potential of the system, ε and σ denote energy and length scales, respectively, and r is the intermolecular distance. The initial velocities of particles form a Maxwell–Boltzmann distribution corresponding to a given temperature.

To keep the system temperature, the following correction is required;νnewiiTDTAwhere νnewi is the

Result and discussion

In this paper, the mechanical properties of nanoscale copper were studied. The mass of an atom, m, is 1.0556×10−25 kg [15]. The pairwise interaction between atoms is described by a Lennard–Jones potential. The interatomic energy and force vanish at a separation of r=2.5σ. The motion equations of the atoms are integrated by the Verlet algorithm with a timestep Δt of 3.64 fs. We consider a perfect nanostructure case, N=960 classical atoms are initially collected on the sites of a face-centered

Conclusions

The tensile and fatigue behavior of nanoscale copper with vacancies at various temperatures has been studied by means of molecular-dynamics simulation. The stress–strain curve for nanoscale copper was obtained. It can be seen from the curve that the tensile stress decreases with increasing vacancy fraction of the material and the maximum stress occurs at about εz=0.6. The nanoscale copper shows very high ultimate tensile stress and elongation rate. In addition, the Young’s modulus for the

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